Weierstrass zeta function
= Weierstrass zeta function
{c}
{title2=$\zeta$}
The Weierstrass zeta function satisfies $\zeta'=-\wp$ and is quasi-periodic: for every period $\omega$, the difference $\zeta(z+\omega)-\zeta(z)$ is constant. It has a simple pole of residue one at each lattice point. Consequently, if $\sum_jc_j=0$, then
$$
\sum_jc_j\zeta(z-a_j)
$$
is an elliptic function.
It is the quasi-periodic zeta member of the <Weierstrass functions>.